Introduction to Flight Simulation (List 2)

Introduction to Flight Simulation (List 2)
Due: 19 october 2010
In this list, we will simulate planets and asteroids. Download the files
vector.h andplanets.cpp and theMakefile from the homepage of the course.
In the main program, the sun is set in the origin with zero speed. Its mass
equals 1.9891.10 30 kg. The mass of the earth equals 5.9736.10 24 kg. Its initial
distance is set at 152098232km from the sun, and its initial speed is set at 29.78
km/s.
1. The gravitational force between two objects with masses m 1 , m 2 , and distance
r is given by the following formula:
F = G m 1m 2
r 2 .
In this formula, G is a constant, the gravity constant. The formula defines
only the strength of the gravitational force, not its direction. The direction
is defined as follows: Both of the masses feel the force F. The first mass
m 1 feels the force in the direction of m 2 . The second mass m 2 feels the
force in the direction of m 1 .
Complete the function computegravity( ) that adds the gravity force
between two objects to the total forces working on the objects.
2. Comlete function method integrate( double h ) of struct object .
At this moment, I do not know how to integrate with a good convergence
order. Just write a primitive algorithm.
3. Complete the program, so that it can simulate the orbit of the earth
around the sun. The time to complete one orbit should be approximately
one year.
4. Add the moon to the system. The mass, speed and distance between the
moon and the earth can be found at Wikipedia.
5. Look up at Wikipedia what is a horseshoe orbit. Add an asteroid to the
solar system, that is in a horse shoe orbit. Take a weight of 1000kg for
the asteroid.
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6. Look up at Wikipedia what are the Lagrangian points. Since it appears
that the points L 4 and L 5 are stable, it must be possible to put an asteroid
in these points. Add an asteroid to the solar system that stays close to
either L 4 or L 5 .
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